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Theorems · Theorem · general topology

OpenPartialHomeomorph.symm_map_nhds_eq

∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  (e : OpenPartialHomeomorph X Y) {x : X}, x ∈ e.source → Filter.map (↑e.symm) (nhds (↑e x)) = nhds x
Defined in
Mathlib.Topology.OpenPartialHomeomorph.Continuity
Cited by
2 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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ChartedSpace.locallyCompactSpace · cited by 5ChartedSpace.locallyCompa…ChartedSpace.locallyConnectedSpace · cited by 0ChartedSpace.locallyConne…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsPartialEquiv.source · cited by 964PartialEquiv.sourcePartialHomeomorph.toPartialEquiv · cited by 917PartialHomeomorph.toParti…OpenPartialHomeomorph.toPartialHomeomorph · cited by 851OpenPartialHomeomorph.toP…Filter.map · cited by 819Filter.mapOpenPartialHomeomorph.toFun' · cited by 745OpenPartialHomeomorph.toF…OpenPartialHomeomorph · cited by 664OpenPartialHomeomorphOpenPartialHomeomorph.symm · cited by 460OpenPartialHomeomorph.symmOpenPartialHomeomorph.left_inv · cited by 78OpenPartialHomeomorph.lef…OpenPartialHomeomorph.map_source · cited by 21OpenPartialHomeomorph.map…OpenPartialHomeomorph.map_nhds_eq · cited by 7OpenPartialHomeomorph.map…OpenPartialHomeomorph.symm_ma…CITED BYCITES

Cites14

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Cited by2

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